If a developer chooses to pull their own app from the itunes store for iOS devices, will the app get deleted from people's phones who may have already installed it the next time they try to sync with their library?
No, Apple will not delete anything from your phone. Apple will also not delete anything from a manual sync with iTunes.
If you backup only to iCloud, lose your phone, buy a new one, you are SOL. When you restore to an iCloud backup, only the apps currently available will come down.
A mathematician is a device for turning coffee into theorems. -- P. Erdos